Classification of monads and moduli components of stable rank 2 bundles with odd determinant and $c_2=10$

Aislan Fontes; Marcos Jardim

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arXiv · 2406.19505

Classification of monads and moduli components of stable rank 2 bundles with odd determinant and $c_2=10$

Aislan Fontes·Marcos Jardim

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Abstract

In this paper, we provide a complete classification of the positive minimal monads whose cohomology is a stable rank 2 bundle on $\mathbb{P}^3$ with Chern classes $c_1=-1, c_2=10$ and we prove the existence of a new irreducible component of the moduli space $\mathcal{B}(-1,10)$ of a rank 2 stable bundles with the given Chern classes. We also show that Hartshorne's conditions on a sequence $\mathcal{X}$ of 10 integers are sufficient and necessary for the existence of a stable rank 2 bundle with odd determinant and spectrum $\mathcal{X}$. Furthermore, we prove that the sequence of integers $\{-2^{n-1},-1,0,1^{n-1}\}$ for $ n\geq4$ is realized as the spectrum of a stable rank 2 bundle $\EE$ of odd determinant by computing the minimal generators of its Rao module.

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BibTeX RIS

Aislan Fontes, Marcos Jardim. 2024-06-27. Classification of monads and moduli components of stable rank 2 bundles with odd determinant and $c_2=10$. https://arxiv.org/abs/2406.19505

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